Radiation pyrometers are instruments capable of non-contact temperature measurements of objects. Pyrometers measure the temperature of an object by measuring the intensity I and/or frequency v of a collected beam of the thermal radiation emitted by an object. Thermal radiation is defined to be the radiation that a body emits when it is at a temperature T. More specifically, the total power P emitted by an object at a temperature T is proportional to εT4, where the emissivity ε is a nonzero constant that may take any positive value less than or equal to 1. Objects that are poor emitters of thermal radiation may have very low emissivities ε. Alternatively, objects with an e of exactly 1 are called black bodies and emit a spectrum of thermal radiation having a distribution of intensities given by the equation
                                          I            ⁡                          (                              v                ,                T                            )                                =                                                    2                ⁢                h                ⁢                                                                  ⁢                                  v                  3                                                            c                2                                      ⁢                          1                                                ⅇ                                      h                    ⁢                                                                                  ⁢                                          v                      /                      k                                        ⁢                                                                                  ⁢                    T                                                  -                1                                                    ,                            (        1        )            where h is Plank's constant, c is the speed of light, k is Boltzmann's constant, T is the temperature of the black body, and v is the frequency of the emitted thermal radiation.
FIG. 1A shows examples of the thermal emission spectra predicted by (1) for a black body at several different temperatures. Further, FIG. 1A shows that a large fraction of the emitted thermal radiation from objects having temperatures in the range of 0-6000° C. is in the infra-red portion of the spectrum. In addition, FIG. 1A shows that as an object is heated, it will begin to emit a higher fraction of its thermal radiation within the visible and high energy (UV, x-rays, etc.) portions of the spectrum.
As stated above, a black body is characterized by an emissivity ε=1. Alternatively, objects that have an emissivity that is less than 1 but otherwise continues to emit according to Plank's law are called grey bodies. In general, however, many real-world objects have emissivities that depend on the frequency v. FIG. 1B shows examples of the thermal emission spectra from a hypothetical black body, a hypothetical grey body, and a hypothetical real object.
Thus, by measuring all of, or even a portion of, the emitted thermal radiation, it becomes possible to infer the temperature of a black body. Alternatively, if the emissivity of the object is known, the temperature of a grey body or real object may be determined by measuring all of, or even a portion of, the emitted thermal radiation.
A typical radiation pyrometer may include an optical system, for example, including one or more lenses and a narrow-pass optical filter. Accordingly, the optical system collects only a small range of frequencies v of the emitted thermal radiation from an object. Furthermore, the optical system has a finite field of view resulting in the collection of a portion, or beam, of emitted thermal radiation. The size and angular divergence of this collection beam depends on the details of the optical system. If the emissivity of the object is well known and the collection beam is narrow enough, the radiation pyrometer may provide a very accurate noncontact measurement of the object's temperature.
Accordingly, pyrometers are often employed to measure temperatures in harsh environments, for example in the high-temperature environments found near and even within various forms of casting furnaces. In practice, pyrometers are calibrated by using known temperatures in the environment that are linked to an energy value measured by the detector. All other temperatures may then be calculated relative to these points via the Planck relation.